Question

Consider all rectangles lying in the region
$\\{(x, y) \in R \times R: 0 \leq x \leq \frac{\pi}{2}\ and\ 0 \leq y \leq 2 \sin (2 x)\\}$
and having one side on the $x$-axis. The area of the rectangle which has the maximum perimeter among all such rectangles, is

• A. $\frac{3 \pi}{2}$
• B. $\pi$
• C. $\frac{\pi}{2 \sqrt{3}}$
• D. $\frac{\pi \sqrt{3}}{2}$

Answer 1

Answer: (C)

$\frac{\pi}{2 \sqrt{3}}$

Answer 2

The area of the rectangle which has the maximum perimeter among all such rectangles, is $\frac{\pi}{2 \sqrt{3}}$